LMFDB - Embedded newform 675.2.e.e.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(226,675)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("675.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1223810289.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 $ x^8 - 2x^7 + 8x^6 - 2x^5 + 23x^4 - 8x^3 + 37x^2 + 15*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$-0.816862 + 1.41485i$ of defining polynomial
Character	$\chi$	$=$	675.451
Dual form			675.2.e.e.226.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.816862 + 1.41485i) q^{2} +(-0.334526 - 0.579416i) q^{4} +(0.252674 - 0.437645i) q^{7} -2.17440 q^{8} +(1.55010 - 2.68485i) q^{11} +(-3.11964 - 5.40337i) q^{13} +(0.412800 + 0.714990i) q^{14} +(2.44524 - 4.23527i) q^{16} -6.10020 q^{17} -5.57022 q^{19} +(2.53244 + 4.38631i) q^{22} +(1.91280 + 3.31307i) q^{23} +10.1932 q^{26} -0.338104 q^{28} +(1.22966 - 2.12984i) q^{29} +(-2.11429 - 3.66206i) q^{31} +(1.82044 + 3.15309i) q^{32} +(4.98302 - 8.63085i) q^{34} -6.72677 q^{37} +(4.55010 - 7.88101i) q^{38} +(-2.72092 - 4.71278i) q^{41} +(0.663704 - 1.14957i) q^{43} -2.07420 q^{44} -6.24997 q^{46} +(1.85396 - 3.21115i) q^{47} +(3.37231 + 5.84101i) q^{49} +(-2.08720 + 3.61514i) q^{52} +2.54205 q^{53} +(-0.549415 + 0.951614i) q^{56} +(2.00893 + 3.47956i) q^{58} +(1.44116 + 2.49616i) q^{59} +(1.42173 - 2.46250i) q^{61} +6.90833 q^{62} +3.83276 q^{64} +(1.20326 + 2.08411i) q^{67} +(2.04068 + 3.53456i) q^{68} -5.54205 q^{71} +11.7988 q^{73} +(5.49484 - 9.51734i) q^{74} +(1.86338 + 3.22748i) q^{76} +(-0.783341 - 1.35679i) q^{77} +(-1.70149 + 2.94707i) q^{79} +8.89047 q^{82} +(6.95059 - 12.0388i) q^{83} +(1.08431 + 1.87808i) q^{86} +(-3.37054 + 5.83795i) q^{88} -3.38513 q^{89} -3.15301 q^{91} +(1.27976 - 2.21661i) q^{92} +(3.02886 + 5.24614i) q^{94} +(5.53779 - 9.59173i) q^{97} -11.0188 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 4 q^{4} + q^{7} - 18 q^{8} - q^{11} - 2 q^{13} + 3 q^{14} - 4 q^{16} - 22 q^{17} + 4 q^{19} - 3 q^{22} + 15 q^{23} + 20 q^{26} - 8 q^{28} + q^{29} + 4 q^{31} + 10 q^{32} - 9 q^{34} - 2 q^{37}+ \cdots - 26 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 4 * q^4 + q^7 - 18 * q^8 - q^11 - 2 * q^13 + 3 * q^14 - 4 * q^16 - 22 * q^17 + 4 * q^19 - 3 * q^22 + 15 * q^23 + 20 * q^26 - 8 * q^28 + q^29 + 4 * q^31 + 10 * q^32 - 9 * q^34 - 2 * q^37 + 23 * q^38 - 5 * q^41 + 10 * q^43 - 44 * q^44 + 20 * q^47 + 3 * q^49 - 17 * q^52 - 40 * q^53 - 30 * q^56 + 18 * q^58 + 17 * q^59 + 13 * q^61 + 12 * q^62 + 38 * q^64 - 17 * q^67 + 34 * q^68 + 16 * q^71 + 4 * q^73 + 40 * q^74 - 11 * q^76 + 12 * q^77 + 7 * q^79 + 24 * q^82 + 30 * q^83 - 34 * q^86 - 9 * q^88 + 18 * q^89 - 34 * q^91 - 12 * q^92 - 3 * q^94 + 19 * q^97 - 26 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.816862	+	1.41485i	−0.577608	+	1.00045i	0.418144	+	0.908381i	$0.362681\pi$
$2$	−0.816862	+	1.41485i	−0.577608	+	1.00045i	−0.995753	+	0.0920666i	$0.970653\pi$
$3$		0			0
$3$		0			0
$4$	−0.334526	−	0.579416i	−0.167263	−	0.289708i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.252674	−	0.437645i	0.0955019	−	0.165414i	−0.814316	−	0.580422i	$-0.802888\pi$
$7$	0.252674	−	0.437645i	0.0955019	−	0.165414i	0.909818	+	0.415008i	$0.136221\pi$
$8$	−2.17440			−0.768767
$9$		0			0
$10$		0			0
$11$	1.55010	−	2.68485i	0.467373	−	0.809514i	−0.531932	−	0.846787i	$-0.678534\pi$
$11$	1.55010	−	2.68485i	0.467373	−	0.809514i	0.999305	+	0.0372730i	$0.0118671\pi$
$12$		0			0
$13$	−3.11964	−	5.40337i	−0.865232	−	1.49863i	−0.866817	−	0.498627i	$-0.833838\pi$
$13$	−3.11964	−	5.40337i	−0.865232	−	1.49863i	0.00158518	−	0.999999i	$-0.499495\pi$
$14$	0.412800	+	0.714990i	0.110325	+	0.191089i
$15$		0			0
$16$	2.44524	−	4.23527i	0.611309	−	1.05882i
$17$	−6.10020			−1.47952			−0.739758	−	0.672873i	$-0.765060\pi$
$17$	−6.10020			−1.47952			−0.739758	+	0.672873i	$0.765060\pi$
$18$		0			0
$19$	−5.57022			−1.27790			−0.638948	−	0.769250i	$-0.720630\pi$
$19$	−5.57022			−1.27790			−0.638948	+	0.769250i	$0.720630\pi$
$20$		0			0
$21$		0			0
$22$	2.53244	+	4.38631i	0.539917	+	0.935164i
$23$	1.91280	+	3.31307i	0.398846	+	0.690822i	0.993584	−	0.113098i	$-0.0360774\pi$
$23$	1.91280	+	3.31307i	0.398846	+	0.690822i	−0.594738	+	0.803920i	$0.702744\pi$
$24$		0			0
$25$		0			0
$26$	10.1932			1.99906
$27$		0			0
$28$	−0.338104			−0.0638957
$29$	1.22966	−	2.12984i	0.228342	−	0.395501i	−0.728975	−	0.684541i	$-0.760003\pi$
$29$	1.22966	−	2.12984i	0.228342	−	0.395501i	0.957317	+	0.289040i	$0.0933361\pi$
$30$		0			0
$31$	−2.11429	−	3.66206i	−0.379738	−	0.657725i	0.611286	−	0.791409i	$-0.290652\pi$
$31$	−2.11429	−	3.66206i	−0.379738	−	0.657725i	−0.991024	+	0.133685i	$0.957319\pi$
$32$	1.82044	+	3.15309i	0.321811	+	0.557394i
$33$		0			0
$34$	4.98302	−	8.63085i	0.854581	−	1.48018i
$35$		0			0
$36$		0			0
$37$	−6.72677			−1.10587			−0.552937	−	0.833223i	$-0.686493\pi$
$37$	−6.72677			−1.10587			−0.552937	+	0.833223i	$0.686493\pi$
$38$	4.55010	−	7.88101i	0.738124	−	1.27847i
$39$		0			0
$40$		0			0
$41$	−2.72092	−	4.71278i	−0.424937	−	0.736012i	0.571478	−	0.820618i	$-0.306370\pi$
$41$	−2.72092	−	4.71278i	−0.424937	−	0.736012i	−0.996415	+	0.0846053i	$0.973037\pi$
$42$		0			0
$43$	0.663704	−	1.14957i	0.101214	−	0.175308i	−0.810971	−	0.585086i	$-0.801061\pi$
$43$	0.663704	−	1.14957i	0.101214	−	0.175308i	0.912185	+	0.409779i	$0.134394\pi$
$44$	−2.07420			−0.312697
$45$		0			0
$46$	−6.24997			−0.921508
$47$	1.85396	−	3.21115i	0.270428	−	0.468395i	−0.698544	−	0.715568i	$-0.746168\pi$
$47$	1.85396	−	3.21115i	0.270428	−	0.468395i	0.968971	+	0.247173i	$0.0795015\pi$
$48$		0			0
$49$	3.37231	+	5.84101i	0.481759	+	0.834431i
$50$		0			0
$51$		0			0
$52$	−2.08720	+	3.61514i	−0.289443	+	0.501329i
$53$	2.54205			0.349177			0.174589	−	0.984641i	$-0.444140\pi$
$53$	2.54205			0.349177			0.174589	+	0.984641i	$0.444140\pi$
$54$		0			0
$55$		0			0
$56$	−0.549415	+	0.951614i	−0.0734187	+	0.127165i
$57$		0			0
$58$	2.00893	+	3.47956i	0.263785	+	0.456889i
$59$	1.44116	+	2.49616i	0.187623	+	0.324973i	0.944457	−	0.328634i	$-0.106588\pi$
$59$	1.44116	+	2.49616i	0.187623	+	0.324973i	−0.756834	+	0.653607i	$0.773255\pi$
$60$		0			0
$61$	1.42173	−	2.46250i	0.182033	−	0.315291i	−0.760539	−	0.649292i	$-0.775065\pi$
$61$	1.42173	−	2.46250i	0.182033	−	0.315291i	0.942573	+	0.334001i	$0.108399\pi$
$62$	6.90833			0.877358
$63$		0			0
$64$	3.83276			0.479095
$65$		0			0
$66$		0			0
$67$	1.20326	+	2.08411i	0.147002	+	0.254614i	0.930118	−	0.367261i	$-0.119704\pi$
$67$	1.20326	+	2.08411i	0.147002	+	0.254614i	−0.783116	+	0.621875i	$0.786371\pi$
$68$	2.04068	+	3.53456i	0.247468	+	0.428628i
$69$		0			0
$70$		0			0
$71$	−5.54205			−0.657720			−0.328860	−	0.944379i	$-0.606664\pi$
$71$	−5.54205			−0.657720			−0.328860	+	0.944379i	$0.606664\pi$
$72$		0			0
$73$	11.7988			1.38095			0.690473	−	0.723359i	$-0.257403\pi$
$73$	11.7988			1.38095			0.690473	+	0.723359i	$0.257403\pi$
$74$	5.49484	−	9.51734i	0.638762	−	1.10637i
$75$		0			0
$76$	1.86338	+	3.22748i	0.213745	+	0.370217i
$77$	−0.783341	−	1.35679i	−0.0892700	−	0.154620i
$78$		0			0
$79$	−1.70149	+	2.94707i	−0.191433	+	0.331571i	−0.945725	−	0.324967i	$-0.894647\pi$
$79$	−1.70149	+	2.94707i	−0.191433	+	0.331571i	0.754293	+	0.656538i	$0.227980\pi$
$80$		0			0
$81$		0			0
$82$	8.89047			0.981789
$83$	6.95059	−	12.0388i	0.762926	−	1.32143i	−0.178410	−	0.983956i	$-0.557095\pi$
$83$	6.95059	−	12.0388i	0.762926	−	1.32143i	0.941336	−	0.337470i	$-0.109571\pi$
$84$		0			0
$85$		0			0
$86$	1.08431	+	1.87808i	0.116924	+	0.202518i
$87$		0			0
$88$	−3.37054	+	5.83795i	−0.359301	+	0.622327i
$89$	−3.38513			−0.358823			−0.179411	−	0.983774i	$-0.557419\pi$
$89$	−3.38513			−0.358823			−0.179411	+	0.983774i	$0.557419\pi$
$90$		0			0
$91$	−3.15301			−0.330525
$92$	1.27976	−	2.21661i	0.133425	−	0.231098i
$93$		0			0
$94$	3.02886	+	5.24614i	0.312403	+	0.541098i
$95$		0			0
$96$		0			0
$97$	5.53779	−	9.59173i	0.562277	−	0.973892i	−0.435020	−	0.900421i	$-0.643259\pi$
$97$	5.53779	−	9.59173i	0.562277	−	0.973892i	0.997297	−	0.0734716i	$-0.0234078\pi$
$98$	−11.0188			−1.11307
$99$		0			0
$100$		0			0
$101$	−8.68451	+	15.0420i	−0.864141	+	1.49674i	0.00375621	+	0.999993i	$0.498804\pi$
$101$	−8.68451	+	15.0420i	−0.864141	+	1.49674i	−0.867897	+	0.496744i	$0.834529\pi$
$102$		0			0
$103$	0.416378	+	0.721188i	0.0410269	+	0.0710608i	0.885810	−	0.464049i	$-0.153604\pi$
$103$	0.416378	+	0.721188i	0.0410269	+	0.0710608i	−0.844783	+	0.535109i	$0.820270\pi$
$104$	6.78334	+	11.7491i	0.665161	+	1.15209i
$105$		0			0
$106$	−2.07650	+	3.59661i	−0.201688	+	0.349334i
$107$	−11.0684			−1.07002			−0.535012	−	0.844844i	$-0.679693\pi$
$107$	−11.0684			−1.07002			−0.535012	+	0.844844i	$0.679693\pi$
$108$		0			0
$109$	−4.65836			−0.446190			−0.223095	−	0.974797i	$-0.571616\pi$
$109$	−4.65836			−0.446190			−0.223095	+	0.974797i	$0.571616\pi$
$110$		0			0
$111$		0			0
$112$	−1.23570	−	2.14029i	−0.116762	−	0.202238i
$113$	5.99711	+	10.3873i	0.564160	+	0.977155i	0.997127	+	0.0757447i	$0.0241334\pi$
$113$	5.99711	+	10.3873i	0.564160	+	0.977155i	−0.432967	+	0.901410i	$0.642533\pi$
$114$		0			0
$115$		0			0
$116$	−1.64542			−0.152773
$117$		0			0
$118$	−4.70892			−0.433491
$119$	−1.54136	+	2.66972i	−0.141297	+	0.244733i
$120$		0			0
$121$	0.694371	+	1.20269i	0.0631246	+	0.109335i
$122$	2.32271	+	4.02305i	0.210288	+	0.364230i
$123$		0			0
$124$	−1.41457	+	2.45011i	−0.127032	+	0.220026i
$125$		0			0
$126$		0			0
$127$	−3.22858			−0.286490			−0.143245	−	0.989687i	$-0.545754\pi$
$127$	−3.22858			−0.286490			−0.143245	+	0.989687i	$0.545754\pi$
$128$	−6.77171	+	11.7289i	−0.598540	+	1.03670i
$129$		0			0
$130$		0			0
$131$	−4.69256	−	8.12776i	−0.409991	−	0.710125i	0.584897	−	0.811107i	$-0.301135\pi$
$131$	−4.69256	−	8.12776i	−0.409991	−	0.710125i	−0.994888	+	0.100982i	$0.967802\pi$
$132$		0			0
$133$	−1.40745	+	2.43778i	−0.122042	+	0.211382i
$134$	−3.93159			−0.339637
$135$		0			0
$136$	13.2643			1.13740
$137$	1.15478	−	2.00013i	0.0986593	−	0.170883i	−0.812471	−	0.583002i	$-0.801878\pi$
$137$	1.15478	−	2.00013i	0.0986593	−	0.170883i	0.911130	+	0.412119i	$0.135211\pi$
$138$		0			0
$139$	−5.44701	−	9.43449i	−0.462009	−	0.800223i	0.537052	−	0.843549i	$-0.319538\pi$
$139$	−5.44701	−	9.43449i	−0.462009	−	0.800223i	−0.999061	+	0.0433260i	$0.986205\pi$
$140$		0			0
$141$		0			0
$142$	4.52709	−	7.84115i	0.379905	−	0.658014i
$143$	−19.3430			−1.61754
$144$		0			0
$145$		0			0
$146$	−9.63799	+	16.6935i	−0.797646	+	1.38156i
$147$		0			0
$148$	2.25028	+	3.89760i	0.184972	+	0.320381i
$149$	−8.17151	−	14.1535i	−0.669436	−	1.15950i	−0.978062	−	0.208314i	$-0.933202\pi$
$149$	−8.17151	−	14.1535i	−0.669436	−	1.15950i	0.308626	−	0.951183i	$-0.400131\pi$
$150$		0			0
$151$	−11.3913	+	19.7304i	−0.927015	+	1.60564i	−0.138727	+	0.990331i	$0.544301\pi$
$151$	−11.3913	+	19.7304i	−0.927015	+	1.60564i	−0.788288	+	0.615306i	$0.789032\pi$
$152$	12.1119			0.982404
$153$		0			0
$154$	2.55953			0.206252
$155$		0			0
$156$		0			0
$157$	−6.23035	−	10.7913i	−0.497236	−	0.861238i	0.502759	−	0.864427i	$-0.332318\pi$
$157$	−6.23035	−	10.7913i	−0.497236	−	0.861238i	−0.999995	+	0.00318877i	$0.998985\pi$
$158$	−2.77976	−	4.81469i	−0.221146	−	0.383036i
$159$		0			0
$160$		0			0
$161$	1.93326			0.152362
$162$		0			0
$163$	−7.57384			−0.593229			−0.296614	−	0.954997i	$-0.595858\pi$
$163$	−7.57384			−0.593229			−0.296614	+	0.954997i	$0.595858\pi$
$164$	−1.82044	+	3.15309i	−0.142152	+	0.246215i
$165$		0			0
$166$	11.3553	+	19.6680i	0.881345	+	1.52653i
$167$	−1.48837	−	2.57793i	−0.115174	−	0.199486i	0.802676	−	0.596416i	$-0.203409\pi$
$167$	−1.48837	−	2.57793i	−0.115174	−	0.199486i	−0.917849	+	0.396929i	$0.870076\pi$
$168$		0			0
$169$	−12.9643	+	22.4548i	−0.997252	+	1.72729i
$170$		0			0
$171$		0			0
$172$	−0.888105			−0.0677174
$173$	−7.92649	+	13.7291i	−0.602640	+	1.04380i	0.389780	+	0.920908i	$0.372551\pi$
$173$	−7.92649	+	13.7291i	−0.602640	+	1.04380i	−0.992420	+	0.122895i	$0.960782\pi$
$174$		0			0
$175$		0			0
$176$	−7.58073	−	13.1302i	−0.571419	−	0.989727i
$177$		0			0
$178$	2.76518	−	4.78943i	0.207259	−	0.358983i
$179$	−17.0841			−1.27693			−0.638463	−	0.769653i	$-0.720429\pi$
$179$	−17.0841			−1.27693			−0.638463	+	0.769653i	$0.720429\pi$
$180$		0			0
$181$	13.3690			0.993712			0.496856	−	0.867833i	$-0.334488\pi$
$181$	13.3690			0.993712			0.496856	+	0.867833i	$0.334488\pi$
$182$	2.57557	−	4.46102i	0.190914	−	0.330673i
$183$		0			0
$184$	−4.15919	−	7.20393i	−0.306620	−	0.531081i
$185$		0			0
$186$		0			0
$187$	−9.45593	+	16.3782i	−0.691486	+	1.19769i
$188$	−2.48079			−0.180930
$189$		0			0
$190$		0			0
$191$	12.6686	−	21.9427i	0.916669	−	1.58772i	0.112230	−	0.993682i	$-0.464201\pi$
$191$	12.6686	−	21.9427i	0.916669	−	1.58772i	0.804439	−	0.594035i	$-0.202466\pi$
$192$		0			0
$193$	4.77976	+	8.27879i	0.344055	+	0.595921i	0.985182	−	0.171515i	$-0.0548660\pi$
$193$	4.77976	+	8.27879i	0.344055	+	0.595921i	−0.641127	+	0.767435i	$0.721533\pi$
$194$	9.04721	+	15.6702i	0.649552	+	1.12506i
$195$		0			0
$196$	2.25625	−	3.90794i	0.161161	−	0.279139i
$197$	2.06841			0.147368			0.0736842	−	0.997282i	$-0.476524\pi$
$197$	2.06841			0.147368			0.0736842	+	0.997282i	$0.476524\pi$
$198$		0			0
$199$	13.0970			0.928419			0.464210	−	0.885725i	$-0.346338\pi$
$199$	13.0970			0.928419			0.464210	+	0.885725i	$0.346338\pi$
$200$		0			0
$201$		0			0
$202$	−14.1881	−	24.5745i	−0.998271	−	1.72906i
$203$	−0.621407	−	1.07631i	−0.0436142	−	0.0755421i
$204$		0			0
$205$		0			0
$206$	−1.36049			−0.0947900
$207$		0			0
$208$	−30.5130			−2.11570
$209$	−8.63441	+	14.9552i	−0.597255	+	1.03448i
$210$		0			0
$211$	−5.55595	−	9.62318i	−0.382487	−	0.662487i	0.608930	−	0.793224i	$-0.291599\pi$
$211$	−5.55595	−	9.62318i	−0.382487	−	0.662487i	−0.991417	+	0.130737i	$0.958266\pi$
$212$	−0.850382	−	1.47291i	−0.0584045	−	0.101160i
$213$		0			0
$214$	9.04136	−	15.6601i	0.618055	−	1.07050i
$215$		0			0
$216$		0			0
$217$	−2.13690			−0.145063
$218$	3.80523	−	6.59086i	0.257723	−	0.446389i
$219$		0			0
$220$		0			0
$221$	19.0304	+	32.9617i	1.28012	+	2.21724i
$222$		0			0
$223$	1.94701	−	3.37231i	0.130381	−	0.225827i	−0.793442	−	0.608645i	$-0.791713\pi$
$223$	1.94701	−	3.37231i	0.130381	−	0.225827i	0.923824	+	0.382819i	$0.125047\pi$
$224$	1.83991			0.122934
$225$		0			0
$226$	−19.5952			−1.30346
$227$	6.40406	−	11.0922i	0.425053	−	0.736213i	−0.571373	−	0.820691i	$-0.693589\pi$
$227$	6.40406	−	11.0922i	0.425053	−	0.736213i	0.996425	+	0.0844781i	$0.0269223\pi$
$228$		0			0
$229$	−3.32647	−	5.76162i	−0.219820	−	0.380739i	0.734933	−	0.678140i	$-0.237214\pi$
$229$	−3.32647	−	5.76162i	−0.219820	−	0.380739i	−0.954753	+	0.297401i	$0.903880\pi$
$230$		0			0
$231$		0			0
$232$	−2.67378	+	4.63112i	−0.175542	+	0.304048i
$233$	3.65836			0.239667			0.119833	−	0.992794i	$-0.461764\pi$
$233$	3.65836			0.239667			0.119833	+	0.992794i	$0.461764\pi$
$234$		0			0
$235$		0			0
$236$	0.964212	−	1.67006i	0.0627648	−	0.108712i
$237$		0			0
$238$	−2.51816	−	4.36158i	−0.163228	−	0.282720i
$239$	−7.84576	−	13.5893i	−0.507500	−	0.879016i	−0.999962	−	0.00868195i	$-0.997236\pi$
$239$	−7.84576	−	13.5893i	−0.507500	−	0.879016i	0.492462	−	0.870334i	$-0.336097\pi$
$240$		0			0
$241$	−5.61248	+	9.72110i	−0.361532	+	0.626191i	−0.988213	−	0.153084i	$-0.951079\pi$
$241$	−5.61248	+	9.72110i	−0.361532	+	0.626191i	0.626681	+	0.779276i	$0.284413\pi$
$242$	−2.26882			−0.145845
$243$		0			0
$244$	−1.90242			−0.121790
$245$		0			0
$246$		0			0
$247$	17.3771	+	30.0980i	1.10568	+	1.91509i
$248$	4.59731	+	7.96278i	0.291930	+	0.505637i
$249$		0			0
$250$		0			0
$251$	−6.94042			−0.438075			−0.219038	−	0.975716i	$-0.570292\pi$
$251$	−6.94042			−0.438075			−0.219038	+	0.975716i	$0.570292\pi$
$252$		0			0
$253$	11.8601			0.745640
$254$	2.63730	−	4.56794i	0.165479	−	0.286618i
$255$		0			0
$256$	−7.23035	−	12.5233i	−0.451897	−	0.782708i
$257$	9.16635	+	15.8766i	0.571781	+	0.990354i	0.996383	+	0.0849739i	$0.0270807\pi$
$257$	9.16635	+	15.8766i	0.571781	+	0.990354i	−0.424602	+	0.905380i	$0.639586\pi$
$258$		0			0
$259$	−1.69968	+	2.94393i	−0.105613	+	0.182927i
$260$		0			0
$261$		0			0
$262$	15.3327			0.947257
$263$	8.03832	−	13.9228i	0.495664	−	0.858515i	−0.504323	−	0.863515i	$-0.668258\pi$
$263$	8.03832	−	13.9228i	0.495664	−	0.858515i	0.999988	+	0.00499942i	$0.00159137\pi$
$264$		0			0
$265$		0			0
$266$	−2.29939	−	3.98265i	−0.140984	−	0.244192i
$267$		0			0
$268$	0.805043	−	1.39438i	0.0491758	−	0.0851751i
$269$	18.2004			1.10970			0.554849	−	0.831951i	$-0.312776\pi$
$269$	18.2004			1.10970			0.554849	+	0.831951i	$0.312776\pi$
$270$		0			0
$271$	−2.48571			−0.150996			−0.0754979	−	0.997146i	$-0.524055\pi$
$271$	−2.48571			−0.150996			−0.0754979	+	0.997146i	$0.524055\pi$
$272$	−14.9164	+	25.8360i	−0.904442	+	1.56654i
$273$		0			0
$274$	1.88659	+	3.26766i	0.113973	+	0.197407i
$275$		0			0
$276$		0			0
$277$	−3.83363	+	6.64004i	−0.230341	+	0.398962i	−0.957908	−	0.287074i	$-0.907317\pi$
$277$	−3.83363	+	6.64004i	−0.230341	+	0.398962i	0.727568	+	0.686036i	$0.240651\pi$
$278$	17.7978			1.06744
$279$		0			0
$280$		0			0
$281$	0.136615	−	0.236624i	0.00814978	−	0.0141158i	−0.861922	−	0.507041i	$-0.830739\pi$
$281$	0.136615	−	0.236624i	0.00814978	−	0.0141158i	0.870072	+	0.492925i	$0.164072\pi$
$282$		0			0
$283$	−1.68544	−	2.91928i	−0.100189	−	0.173533i	0.811573	−	0.584251i	$-0.198611\pi$
$283$	−1.68544	−	2.91928i	−0.100189	−	0.173533i	−0.911763	+	0.410718i	$0.865278\pi$
$284$	1.85396	+	3.21115i	0.110012	+	0.190547i
$285$		0			0
$286$	15.8006	−	27.3674i	0.934307	−	1.61827i
$287$	−2.75003			−0.162329
$288$		0			0
$289$	20.2125			1.18897
$290$		0			0
$291$		0			0
$292$	−3.94701	−	6.83642i	−0.230981	−	0.400071i
$293$	−2.82202	−	4.88788i	−0.164864	−	0.285553i	0.771743	−	0.635935i	$-0.219385\pi$
$293$	−2.82202	−	4.88788i	−0.164864	−	0.285553i	−0.936607	+	0.350382i	$0.886052\pi$
$294$		0			0
$295$		0			0
$296$	14.6267			0.850159
$297$		0			0
$298$	26.7000			1.54669
$299$	11.9345	−	20.6711i	0.690189	−	1.19544i
$300$		0			0
$301$	−0.335402	−	0.580933i	−0.0193322	−	0.0334844i
$302$	−18.6103	−	32.2340i	−1.07090	−	1.85486i
$303$		0			0
$304$	−13.6205	+	23.5914i	−0.781190	+	1.35306i
$305$		0			0
$306$		0			0
$307$	5.44105			0.310537			0.155269	−	0.987872i	$-0.450376\pi$
$307$	5.44105			0.310537			0.155269	+	0.987872i	$0.450376\pi$
$308$	−0.524096	+	0.907761i	−0.0298632	+	0.0517245i
$309$		0			0
$310$		0			0
$311$	−9.53985	−	16.5235i	−0.540955	−	0.936962i	−0.998849	−	0.0479550i	$-0.984730\pi$
$311$	−9.53985	−	16.5235i	−0.540955	−	0.936962i	0.457895	−	0.889007i	$-0.348604\pi$
$312$		0			0
$313$	4.57116	−	7.91747i	0.258377	−	0.447522i	−0.707430	−	0.706783i	$-0.750146\pi$
$313$	4.57116	−	7.91747i	0.258377	−	0.447522i	0.965807	+	0.259261i	$0.0834790\pi$
$314$	20.3573			1.14883
$315$		0			0
$316$	2.27677			0.128078
$317$	7.11836	−	12.3294i	0.399807	−	0.692486i	−0.593895	−	0.804543i	$-0.702410\pi$
$317$	7.11836	−	12.3294i	0.399807	−	0.692486i	0.993702	+	0.112056i	$0.0357437\pi$
$318$		0			0
$319$	−3.81220	−	6.60292i	−0.213442	−	0.369693i
$320$		0			0
$321$		0			0
$322$	−1.57921	+	2.73527i	−0.0880057	+	0.152430i
$323$	33.9795			1.89067
$324$		0			0
$325$		0			0
$326$	6.18678	−	10.7158i	0.342654	−	0.593494i
$327$		0			0
$328$	5.91638	+	10.2475i	0.326677	+	0.565822i
$329$	−0.936896	−	1.62275i	−0.0516527	−	0.0894652i
$330$		0			0
$331$	6.10001	−	10.5655i	0.335287	−	0.580734i	−0.648253	−	0.761425i	$-0.724500\pi$
$331$	6.10001	−	10.5655i	0.335287	−	0.580734i	0.983540	+	0.180691i	$0.0578334\pi$
$332$	−9.30061			−0.510437
$333$		0			0
$334$	4.86317			0.266101
$335$		0			0
$336$		0			0
$337$	−2.29493	−	3.97494i	−0.125013	−	0.216529i	0.796725	−	0.604342i	$-0.206564\pi$
$337$	−2.29493	−	3.97494i	−0.125013	−	0.216529i	−0.921738	+	0.387813i	$0.873231\pi$
$338$	−21.1800	−	36.6849i	−1.15204	−	1.99540i
$339$		0			0
$340$		0			0
$341$	−13.1094			−0.709917
$342$		0			0
$343$	6.94582			0.375039
$344$	−1.44316	+	2.49962i	−0.0778099	+	0.134771i
$345$		0			0
$346$	−12.9497	−	22.4295i	−0.696180	−	1.20582i
$347$	16.7301	+	28.9775i	0.898121	+	1.55559i	0.829894	+	0.557921i	$0.188401\pi$
$347$	16.7301	+	28.9775i	0.898121	+	1.55559i	0.0682272	+	0.997670i	$0.478266\pi$
$348$		0			0
$349$	14.0408	−	24.3193i	0.751586	−	1.30178i	−0.195468	−	0.980710i	$-0.562623\pi$
$349$	14.0408	−	24.3193i	0.751586	−	1.30178i	0.947054	−	0.321074i	$-0.104044\pi$
$350$		0			0
$351$		0			0
$352$	11.2875			0.601624
$353$	−0.920851	+	1.59496i	−0.0490119	+	0.0848912i	−0.889491	−	0.456954i	$-0.848941\pi$
$353$	−0.920851	+	1.59496i	−0.0490119	+	0.0848912i	0.840479	+	0.541845i	$0.182274\pi$
$354$		0			0
$355$		0			0
$356$	1.13241	+	1.96140i	0.0600178	+	0.103954i
$357$		0			0
$358$	13.9553	−	24.1714i	0.737563	−	1.27750i
$359$	12.1119			0.639241			0.319621	−	0.947546i	$-0.396445\pi$
$359$	12.1119			0.639241			0.319621	+	0.947546i	$0.396445\pi$
$360$		0			0
$361$	12.0274			0.633020
$362$	−10.9206	+	18.9151i	−0.573976	+	0.994156i
$363$		0			0
$364$	1.05476	+	1.82690i	0.0552846	+	0.0957558i
$365$		0			0
$366$		0			0
$367$	7.28688	−	12.6212i	0.380372	−	0.658824i	−0.610743	−	0.791829i	$-0.709129\pi$
$367$	7.28688	−	12.6212i	0.380372	−	0.658824i	0.991115	+	0.133005i	$0.0424626\pi$
$368$	18.7090			0.975274
$369$		0			0
$370$		0			0
$371$	0.642310	−	1.11251i	0.0333471	−	0.0577589i
$372$		0			0
$373$	4.72323	+	8.18087i	0.244560	+	0.423590i	0.962008	−	0.273022i	$-0.0880233\pi$
$373$	4.72323	+	8.18087i	0.244560	+	0.423590i	−0.717448	+	0.696612i	$0.754690\pi$
$374$	−15.4484	−	26.7574i	−0.798817	−	1.38359i
$375$		0			0
$376$	−4.03125	+	6.98233i	−0.207896	+	0.360086i
$377$	−15.3444			−0.790276
$378$		0			0
$379$	−28.5541			−1.46673			−0.733363	−	0.679837i	$-0.762051\pi$
$379$	−28.5541			−1.46673			−0.733363	+	0.679837i	$0.762051\pi$
$380$		0			0
$381$		0			0
$382$	20.6970	+	35.8483i	1.05895	+	1.83416i
$383$	0.732704	+	1.26908i	0.0374394	+	0.0648470i	0.884138	−	0.467226i	$-0.154747\pi$
$383$	0.732704	+	1.26908i	0.0374394	+	0.0648470i	−0.846699	+	0.532073i	$0.821413\pi$
$384$		0			0
$385$		0			0
$386$	−15.6176			−0.794916
$387$		0			0
$388$	−7.41014			−0.376193
$389$	−6.45506	+	11.1805i	−0.327284	+	0.566873i	−0.981972	−	0.189026i	$-0.939467\pi$
$389$	−6.45506	+	11.1805i	−0.327284	+	0.566873i	0.654688	+	0.755900i	$0.272800\pi$
$390$		0			0
$391$	−11.6685	−	20.2104i	−0.590100	−	1.02208i
$392$	−7.33276	−	12.7007i	−0.370360	−	0.641483i
$393$		0			0
$394$	−1.68961	+	2.92649i	−0.0851212	+	0.147434i
$395$		0			0
$396$		0			0
$397$	−0.868386			−0.0435831			−0.0217915	−	0.999763i	$-0.506937\pi$
$397$	−0.868386			−0.0435831			−0.0217915	+	0.999763i	$0.506937\pi$
$398$	−10.6984	+	18.5302i	−0.536263	+	0.928834i
$399$		0			0
$400$		0			0
$401$	16.7063	+	28.9361i	0.834270	+	1.44500i	0.894623	+	0.446822i	$0.147444\pi$
$401$	16.7063	+	28.9361i	0.834270	+	1.44500i	−0.0603527	+	0.998177i	$0.519223\pi$
$402$		0			0
$403$	−13.1916	+	22.8486i	−0.657122	+	1.13817i
$404$	11.6208			0.578156
$405$		0			0
$406$	2.03042			0.100768
$407$	−10.4272	+	18.0604i	−0.516856	+	0.895221i
$408$		0			0
$409$	−2.52767	−	4.37806i	−0.124985	−	0.216481i	0.796742	−	0.604320i	$-0.206555\pi$
$409$	−2.52767	−	4.37806i	−0.124985	−	0.216481i	−0.921727	+	0.387839i	$0.873222\pi$
$410$		0			0
$411$		0			0
$412$	0.278579	−	0.482512i	0.0137246	−	0.0237717i
$413$	1.45658			0.0716734
$414$		0			0
$415$		0			0
$416$	11.3582	−	19.6730i	0.556883	−	0.964549i
$417$		0			0
$418$	−14.1062	−	24.4327i	−0.689959	−	1.19504i
$419$	5.47880	+	9.48955i	0.267657	+	0.463595i	0.968256	−	0.249960i	$-0.0804174\pi$
$419$	5.47880	+	9.48955i	0.267657	+	0.463595i	−0.700600	+	0.713555i	$0.747084\pi$
$420$		0			0
$421$	5.31932	−	9.21333i	0.259248	−	0.449030i	−0.706793	−	0.707421i	$-0.749859\pi$
$421$	5.31932	−	9.21333i	0.259248	−	0.449030i	0.966041	+	0.258390i	$0.0831921\pi$
$422$	18.1538			0.883711
$423$		0			0
$424$	−5.52744			−0.268436
$425$		0			0
$426$		0			0
$427$	−0.718467	−	1.24442i	−0.0347691	−	0.0602218i
$428$	3.70267	+	6.41322i	0.178975	+	0.309995i
$429$		0			0
$430$		0			0
$431$	37.3529			1.79923			0.899613	−	0.436687i	$-0.143848\pi$
$431$	37.3529			1.79923			0.899613	+	0.436687i	$0.143848\pi$
$432$		0			0
$433$	−17.2125			−0.827179			−0.413589	−	0.910464i	$-0.635725\pi$
$433$	−17.2125			−0.827179			−0.413589	+	0.910464i	$0.635725\pi$
$434$	1.74556	−	3.02339i	0.0837894	−	0.145127i
$435$		0			0
$436$	1.55834	+	2.69913i	0.0746310	+	0.129265i
$437$	−10.6547	−	18.4545i	−0.509684	−	0.882799i
$438$		0			0
$439$	15.8744	−	27.4952i	0.757642	−	1.31228i	−0.186408	−	0.982473i	$-0.559684\pi$
$439$	15.8744	−	27.4952i	0.757642	−	1.31228i	0.944050	−	0.329803i	$-0.106982\pi$
$440$		0			0
$441$		0			0
$442$	−62.1809			−2.95764
$443$	−0.177979	+	0.308268i	−0.00845603	+	0.0146463i	−0.870222	−	0.492659i	$-0.836025\pi$
$443$	−0.177979	+	0.308268i	−0.00845603	+	0.0146463i	0.861766	+	0.507305i	$0.169358\pi$
$444$		0			0
$445$		0			0
$446$	3.18087	+	5.50943i	0.150619	+	0.260879i
$447$		0			0
$448$	0.968438	−	1.67738i	0.0457544	−	0.0792490i
$449$	7.85632			0.370762			0.185381	−	0.982667i	$-0.440648\pi$
$449$	7.85632			0.370762			0.185381	+	0.982667i	$0.440648\pi$
$450$		0			0
$451$	−16.8708			−0.794416
$452$	4.01238	−	6.94964i	0.188726	−	0.326884i
$453$		0			0
$454$	10.4625	+	18.1215i	0.491028	+	0.850485i
$455$		0			0
$456$		0			0
$457$	−10.7455	+	18.6118i	−0.502654	+	0.870622i	0.497341	+	0.867555i	$0.334310\pi$
$457$	−10.7455	+	18.6118i	−0.502654	+	0.870622i	−0.999995	+	0.00306742i	$0.999024\pi$
$458$	10.8691			0.507879
$459$		0			0
$460$		0			0
$461$	20.4964	−	35.5007i	0.954611	−	1.65343i	0.219355	−	0.975645i	$-0.429605\pi$
$461$	20.4964	−	35.5007i	0.954611	−	1.65343i	0.735256	−	0.677789i	$-0.237062\pi$
$462$		0			0
$463$	−21.0669	−	36.4890i	−0.979063	−	1.69579i	−0.665816	−	0.746116i	$-0.731916\pi$
$463$	−21.0669	−	36.4890i	−0.979063	−	1.69579i	−0.313248	−	0.949671i	$-0.601417\pi$
$464$	−6.01363	−	10.4159i	−0.279176	−	0.483546i
$465$		0			0
$466$	−2.98837	+	5.17601i	−0.138434	+	0.239774i
$467$	22.5376			1.04292			0.521459	−	0.853276i	$-0.325388\pi$
$467$	22.5376			1.04292			0.521459	+	0.853276i	$0.325388\pi$
$468$		0			0
$469$	1.21613			0.0561557
$470$		0			0
$471$		0			0
$472$	−3.13366	−	5.42766i	−0.144238	−	0.249828i
$473$	−2.05762	−	3.56390i	−0.0946093	−	0.163868i
$474$		0			0
$475$		0			0
$476$	2.06251			0.0945348
$477$		0			0
$478$	25.6356			1.17255
$479$	−16.6440	+	28.8282i	−0.760483	+	1.31720i	0.182119	+	0.983277i	$0.441704\pi$
$479$	−16.6440	+	28.8282i	−0.760483	+	1.31720i	−0.942602	+	0.333919i	$0.891629\pi$
$480$		0			0
$481$	20.9851	+	36.3472i	0.956837	+	1.65729i
$482$	−9.16924	−	15.8816i	−0.417647	−	0.723387i
$483$		0			0
$484$	0.464570	−	0.804660i	0.0211168	−	0.0365754i
$485$		0			0
$486$		0			0
$487$	23.7703			1.07713			0.538566	−	0.842583i	$-0.318966\pi$
$487$	23.7703			1.07713			0.538566	+	0.842583i	$0.318966\pi$
$488$	−3.09140	+	5.35447i	−0.139941	+	0.242385i
$489$		0			0
$490$		0			0
$491$	−2.30281	−	3.98859i	−0.103925	−	0.180003i	0.809374	−	0.587294i	$-0.199807\pi$
$491$	−2.30281	−	3.98859i	−0.103925	−	0.180003i	−0.913298	+	0.407291i	$0.866473\pi$
$492$		0			0
$493$	−7.50118	+	12.9924i	−0.337836	+	0.585150i
$494$	−56.7787			−2.55459
$495$		0			0
$496$	−20.6797			−0.928548
$497$	−1.40033	+	2.42545i	−0.0628135	+	0.108796i
$498$		0			0
$499$	9.44878	+	16.3658i	0.422985	+	0.732632i	0.996230	−	0.0867522i	$-0.0276488\pi$
$499$	9.44878	+	16.3658i	0.422985	+	0.732632i	−0.573245	+	0.819384i	$0.694316\pi$
$500$		0			0
$501$		0			0
$502$	5.66936	−	9.81962i	0.253036	−	0.438271i
$503$	−35.7581			−1.59438			−0.797188	−	0.603731i	$-0.793680\pi$
$503$	−35.7581			−1.59438			−0.797188	+	0.603731i	$0.793680\pi$
$504$		0			0
$505$		0			0
$506$	−9.68809	+	16.7803i	−0.430688	+	0.745974i
$507$		0			0
$508$	1.08004	+	1.87069i	0.0479192	+	0.0829985i
$509$	12.2034	+	21.1368i	0.540904	+	0.936874i	0.998852	+	0.0478949i	$0.0152513\pi$
$509$	12.2034	+	21.1368i	0.540904	+	0.936874i	−0.457948	+	0.888979i	$0.651415\pi$
$510$		0			0
$511$	2.98125	−	5.16368i	0.131883	−	0.228428i
$512$	−3.46207			−0.153003
$513$		0			0
$514$	−29.9506			−1.32106
$515$		0			0
$516$		0			0
$517$	−5.74765	−	9.95523i	−0.252782	−	0.437830i
$518$	−2.77681	−	4.80957i	−0.122006	−	0.211321i
$519$		0			0
$520$		0			0
$521$	−33.3968			−1.46314			−0.731571	−	0.681766i	$-0.761212\pi$
$521$	−33.3968			−1.46314			−0.731571	+	0.681766i	$0.761212\pi$
$522$		0			0
$523$	−37.3654			−1.63388			−0.816938	−	0.576726i	$-0.804330\pi$
$523$	−37.3654			−1.63388			−0.816938	+	0.576726i	$0.804330\pi$
$524$	−3.13957	+	5.43789i	−0.137153	+	0.237555i
$525$		0			0
$526$	13.1324	+	22.7460i	0.572600	+	0.991772i
$527$	12.8976	+	22.3393i	0.561828	+	0.973115i
$528$		0			0
$529$	4.18239	−	7.24412i	0.181843	−	0.314962i
$530$		0			0
$531$		0			0
$532$	1.88332			0.0816521
$533$	−16.9766	+	29.4043i	−0.735338	+	1.27364i
$534$		0			0
$535$		0			0
$536$	−2.61637	−	4.53168i	−0.113010	−	0.195739i
$537$		0			0
$538$	−14.8672	+	25.7508i	−0.640971	+	1.11019i
$539$	20.9097			0.900645
$540$		0			0
$541$	28.2560			1.21482			0.607409	−	0.794389i	$-0.292209\pi$
$541$	28.2560			1.21482			0.607409	+	0.794389i	$0.292209\pi$
$542$	2.03048	−	3.51689i	0.0872165	−	0.151063i
$543$		0			0
$544$	−11.1051	−	19.2345i	−0.476125	−	0.824673i
$545$		0			0
$546$		0			0
$547$	19.2726	−	33.3811i	0.824036	−	1.42727i	−0.0786172	−	0.996905i	$-0.525050\pi$
$547$	19.2726	−	33.3811i	0.824036	−	1.42727i	0.902654	−	0.430368i	$-0.141616\pi$
$548$	−1.54521			−0.0660082
$549$		0			0
$550$		0			0
$551$	−6.84949	+	11.8637i	−0.291798	+	0.505409i
$552$		0			0
$553$	0.859845	+	1.48929i	0.0365643	+	0.0633313i
$554$	−6.26309	−	10.8480i	−0.266093	−	0.460887i
$555$		0			0
$556$	−3.64433	+	6.31217i	−0.154554	+	0.267696i
$557$	27.4125			1.16151			0.580753	−	0.814080i	$-0.302758\pi$
$557$	27.4125			1.16151			0.580753	+	0.814080i	$0.302758\pi$
$558$		0			0
$559$	−8.28206			−0.350294
$560$		0			0
$561$		0			0
$562$	0.223191	+	0.386579i	0.00941476	+	0.0163068i
$563$	−13.8196	−	23.9363i	−0.582427	−	1.00879i	−0.995191	−	0.0979551i	$-0.968770\pi$
$563$	−13.8196	−	23.9363i	−0.582427	−	1.00879i	0.412764	−	0.910838i	$-0.364563\pi$
$564$		0			0
$565$		0			0
$566$	5.50710			0.231481
$567$		0			0
$568$	12.0506			0.505634
$569$	−7.35807	+	12.7446i	−0.308467	+	0.534280i	−0.978027	−	0.208478i	$-0.933149\pi$
$569$	−7.35807	+	12.7446i	−0.308467	+	0.534280i	0.669561	+	0.742757i	$0.266482\pi$
$570$		0			0
$571$	14.1503	+	24.5090i	0.592172	+	1.02567i	0.993939	+	0.109930i	$0.0350627\pi$
$571$	14.1503	+	24.5090i	0.592172	+	1.02567i	−0.401768	+	0.915742i	$0.631604\pi$
$572$	6.47074	+	11.2077i	0.270555	+	0.468616i
$573$		0			0
$574$	2.24639	−	3.89087i	0.0937626	−	0.162402i
$575$		0			0
$576$		0			0
$577$	−40.7976			−1.69843			−0.849214	−	0.528049i	$-0.822924\pi$
$577$	−40.7976			−1.69843			−0.849214	+	0.528049i	$0.822924\pi$
$578$	−16.5108	+	28.5975i	−0.686759	+	1.18950i
$579$		0			0
$580$		0			0
$581$	−3.51247	−	6.08377i	−0.145722	−	0.252397i
$582$		0			0
$583$	3.94044	−	6.82504i	0.163196	−	0.282664i
$584$	−25.6553			−1.06162
$585$		0			0
$586$	9.22080			0.380908
$587$	1.39016	−	2.40784i	0.0573782	−	0.0993820i	−0.835910	−	0.548867i	$-0.815059\pi$
$587$	1.39016	−	2.40784i	0.0573782	−	0.0993820i	0.893288	+	0.449485i	$0.148393\pi$
$588$		0			0
$589$	11.7771	+	20.3985i	0.485265	+	0.840504i
$590$		0			0
$591$		0			0
$592$	−16.4485	+	28.4897i	−0.676031	+	1.17092i
$593$	14.8084			0.608109			0.304055	−	0.952655i	$-0.401659\pi$
$593$	14.8084			0.608109			0.304055	+	0.952655i	$0.401659\pi$
$594$		0			0
$595$		0			0
$596$	−5.46717	+	9.46941i	−0.223944	+	0.387882i
$597$		0			0
$598$	19.4976	+	33.7709i	0.797318	+	1.38100i
$599$	−8.17151	−	14.1535i	−0.333879	−	0.578295i	0.649390	−	0.760456i	$-0.275024\pi$
$599$	−8.17151	−	14.1535i	−0.333879	−	0.578295i	−0.983269	+	0.182160i	$0.941691\pi$
$600$		0			0
$601$	3.31185	−	5.73630i	0.135093	−	0.233988i	−0.790540	−	0.612411i	$-0.790200\pi$
$601$	3.31185	−	5.73630i	0.135093	−	0.233988i	0.925633	+	0.378422i	$0.123533\pi$
$602$	1.09591			0.0446658
$603$		0			0
$604$	15.2428			0.620221
$605$		0			0
$606$		0			0
$607$	−15.1547	−	26.2487i	−0.615110	−	1.06540i	−0.990365	−	0.138480i	$-0.955778\pi$
$607$	−15.1547	−	26.2487i	−0.615110	−	1.06540i	0.375256	−	0.926921i	$-0.377555\pi$
$608$	−10.1403	−	17.5634i	−0.411242	−	0.712291i
$609$		0			0
$610$		0			0
$611$	−23.1347			−0.935931
$612$		0			0
$613$	14.7803			0.596969			0.298484	−	0.954415i	$-0.403519\pi$
$613$	14.7803			0.596969			0.298484	+	0.954415i	$0.403519\pi$
$614$	−4.44459	+	7.69825i	−0.179369	+	0.310676i
$615$		0			0
$616$	1.70330	+	2.95020i	0.0686278	+	0.118867i
$617$	−16.9256	−	29.3160i	−0.681399	−	1.18022i	−0.974554	−	0.224152i	$-0.928039\pi$
$617$	−16.9256	−	29.3160i	−0.681399	−	1.18022i	0.293155	−	0.956065i	$-0.405295\pi$
$618$		0			0
$619$	−5.84433	+	10.1227i	−0.234903	+	0.406865i	−0.959245	−	0.282577i	$-0.908811\pi$
$619$	−5.84433	+	10.1227i	−0.234903	+	0.406865i	0.724341	+	0.689442i	$0.242144\pi$
$620$		0			0
$621$		0			0
$622$	31.1709			1.24984
$623$	−0.855334	+	1.48148i	−0.0342682	+	0.0593543i
$624$		0			0
$625$		0			0
$626$	7.46800	+	12.9350i	0.298481	+	0.516985i
$627$		0			0
$628$	−4.16843	+	7.21993i	−0.166338	+	0.288107i
$629$	41.0347			1.63616
$630$		0			0
$631$	−38.1357			−1.51816			−0.759078	−	0.650999i	$-0.774350\pi$
$631$	−38.1357			−1.51816			−0.759078	+	0.650999i	$0.774350\pi$
$632$	3.69972	−	6.40810i	0.147167	−	0.254901i
$633$		0			0
$634$	11.6294	+	20.1428i	0.461864	+	0.799972i
$635$		0			0
$636$		0			0
$637$	21.0408	−	36.4437i	0.833666	−	1.44395i
$638$	12.4562			0.493144
$639$		0			0
$640$		0			0
$641$	−17.3827	+	30.1077i	−0.686576	+	1.18918i	0.286363	+	0.958121i	$0.407554\pi$
$641$	−17.3827	+	30.1077i	−0.686576	+	1.18918i	−0.972939	+	0.231063i	$0.925780\pi$
$642$		0			0
$643$	−1.34258	−	2.32541i	−0.0529461	−	0.0917053i	0.838338	−	0.545151i	$-0.183528\pi$
$643$	−1.34258	−	2.32541i	−0.0529461	−	0.0917053i	−0.891284	+	0.453446i	$0.850194\pi$
$644$	−0.646726	−	1.12016i	−0.0254846	−	0.0441406i
$645$		0			0
$646$	−27.7565	+	48.0757i	−1.09207	+	1.89151i
$647$	−40.5103			−1.59262			−0.796311	−	0.604887i	$-0.793218\pi$
$647$	−40.5103			−1.59262			−0.796311	+	0.604887i	$0.793218\pi$
$648$		0			0
$649$	8.93578			0.350760
$650$		0			0
$651$		0			0
$652$	2.53365	+	4.38841i	0.0992253	+	0.171863i
$653$	6.66772	+	11.5488i	0.260928	+	0.451941i	0.966489	−	0.256709i	$-0.0826381\pi$
$653$	6.66772	+	11.5488i	0.260928	+	0.451941i	−0.705561	+	0.708650i	$0.749305\pi$
$654$		0			0
$655$		0			0
$656$	−26.6132			−1.03907
$657$		0			0
$658$	3.06126			0.119340
$659$	15.5772	−	26.9804i	0.606800	−	1.05101i	−0.384965	−	0.922931i	$-0.625786\pi$
$659$	15.5772	−	26.9804i	0.606800	−	1.05101i	0.991764	−	0.128077i	$-0.0408803\pi$
$660$		0			0
$661$	−3.15894	−	5.47145i	−0.122869	−	0.212815i	0.798029	−	0.602619i	$-0.205876\pi$
$661$	−3.15894	−	5.47145i	−0.122869	−	0.212815i	−0.920898	+	0.389804i	$0.872543\pi$
$662$	9.96574	+	17.2612i	0.387329	+	0.670874i
$663$		0			0
$664$	−15.1134	+	26.1771i	−0.586512	+	1.01587i
$665$		0			0
$666$		0			0
$667$	9.40838			0.364294
$668$	−0.995798	+	1.72477i	−0.0385286	+	0.0667334i
$669$		0			0
$670$		0			0
$671$	−4.40764	−	7.63426i	−0.170155	−	0.294717i
$672$		0			0
$673$	3.29610	−	5.70901i	0.127055	−	0.220066i	−0.795479	−	0.605981i	$-0.792781\pi$
$673$	3.29610	−	5.70901i	0.127055	−	0.220066i	0.922534	+	0.385915i	$0.126114\pi$
$674$	7.49857			0.288834
$675$		0			0
$676$	17.3476			0.667214
$677$	17.4473	−	30.2197i	0.670556	−	1.16144i	−0.307191	−	0.951648i	$-0.599389\pi$
$677$	17.4473	−	30.2197i	0.670556	−	1.16144i	0.977747	−	0.209788i	$-0.0672775\pi$
$678$		0			0
$679$	−2.79851	−	4.84716i	−0.107397	−	0.186017i
$680$		0			0
$681$		0			0
$682$	10.7086	−	18.5479i	0.410054	−	0.710234i
$683$	−26.0958			−0.998528			−0.499264	−	0.866450i	$-0.666396\pi$
$683$	−26.0958			−0.998528			−0.499264	+	0.866450i	$0.666396\pi$
$684$		0			0
$685$		0			0
$686$	−5.67378	+	9.82727i	−0.216626	+	0.375207i
$687$		0			0
$688$	−3.24583	−	5.62194i	−0.123746	−	0.214334i
$689$	−7.93028	−	13.7356i	−0.302119	−	0.523286i
$690$		0			0
$691$	14.6529	−	25.3796i	0.557423	−	0.965485i	−0.440288	−	0.897857i	$-0.645124\pi$
$691$	14.6529	−	25.3796i	0.557423	−	0.965485i	0.997711	−	0.0676282i	$-0.0215432\pi$
$692$	10.6065			0.403197
$693$		0			0
$694$	−54.6648			−2.07505
$695$		0			0
$696$		0			0
$697$	16.5982	+	28.7489i	0.628701	+	1.08894i
$698$	22.9387	+	39.7311i	0.868244	+	1.50384i
$699$		0			0
$700$		0			0
$701$	−15.3891			−0.581239			−0.290620	−	0.956839i	$-0.593861\pi$
$701$	−15.3891			−0.581239			−0.290620	+	0.956839i	$0.593861\pi$
$702$		0			0
$703$	37.4696			1.41319
$704$	5.94116	−	10.2904i	0.223916	−	0.387834i
$705$		0			0
$706$	−1.50442	−	2.60572i	−0.0566194	−	0.0980677i
$707$	4.38870	+	7.60146i	0.165054	+	0.285882i
$708$		0			0
$709$	3.86996	−	6.70296i	0.145339	−	0.251735i	−0.784160	−	0.620558i	$-0.786906\pi$
$709$	3.86996	−	6.70296i	0.145339	−	0.251735i	0.929499	+	0.368823i	$0.120239\pi$
$710$		0			0
$711$		0			0
$712$	7.36062			0.275851
$713$	8.08842	−	14.0096i	0.302914	−	0.524662i
$714$		0			0
$715$		0			0
$716$	5.71508	+	9.89880i	0.213582	+	0.369936i
$717$		0			0
$718$	−9.89374	+	17.1365i	−0.369231	+	0.639527i
$719$	15.1316			0.564313			0.282156	−	0.959368i	$-0.408950\pi$
$719$	15.1316			0.564313			0.282156	+	0.959368i	$0.408950\pi$
$720$		0			0
$721$	0.420832			0.0156726
$722$	−9.82470	+	17.0169i	−0.365638	+	0.633303i
$723$		0			0
$724$	−4.47229	−	7.74623i	−0.166211	−	0.287886i
$725$		0			0
$726$		0			0
$727$	−0.0809381	+	0.140189i	−0.00300183	+	0.00519932i	−0.867522	−	0.497398i	$-0.834289\pi$
$727$	−0.0809381	+	0.140189i	−0.00300183	+	0.00519932i	0.864521	+	0.502597i	$0.167622\pi$
$728$	6.85590			0.254097
$729$		0			0
$730$		0			0
$731$	−4.04873	+	7.01260i	−0.149748	+	0.259370i
$732$		0			0
$733$	25.0166	+	43.3300i	0.924009	+	1.60043i	0.793148	+	0.609029i	$0.208441\pi$
$733$	25.0166	+	43.3300i	0.924009	+	1.60043i	0.130861	+	0.991401i	$0.458226\pi$
$734$	11.9047	+	20.6196i	0.439412	+	0.761084i
$735$		0			0
$736$	−6.96427	+	12.0625i	−0.256707	+	0.444629i
$737$	7.46070			0.274818
$738$		0			0
$739$	30.5505			1.12382			0.561909	−	0.827199i	$-0.310067\pi$
$739$	30.5505			1.12382			0.561909	+	0.827199i	$0.310067\pi$
$740$		0			0
$741$		0			0
$742$	1.04936	+	1.81754i	0.0385231	+	0.0667240i
$743$	2.98342	+	5.16743i	0.109451	+	0.189575i	0.915548	−	0.402209i	$-0.131757\pi$
$743$	2.98342	+	5.16743i	0.109451	+	0.189575i	−0.806097	+	0.591783i	$0.798424\pi$
$744$		0			0
$745$		0			0
$746$	−15.4329			−0.565039
$747$		0			0
$748$	12.6530			0.462640
$749$	−2.79670	+	4.84403i	−0.102189	+	0.176997i
$750$		0			0
$751$	−17.1988	−	29.7892i	−0.627593	−	1.08702i	−0.988033	−	0.154240i	$-0.950707\pi$
$751$	−17.1988	−	29.7892i	−0.627593	−	1.08702i	0.360441	−	0.932782i	$-0.382626\pi$
$752$	−9.06674	−	15.7041i	−0.330630	−	0.572668i
$753$		0			0
$754$	12.5342	−	21.7099i	0.456470	−	0.790630i
$755$		0			0
$756$		0			0
$757$	40.6873			1.47881			0.739403	−	0.673263i	$-0.235108\pi$
$757$	40.6873			1.47881			0.739403	+	0.673263i	$0.235108\pi$
$758$	23.3248	−	40.3997i	0.847194	−	1.46738i
$759$		0			0
$760$		0			0
$761$	14.1298	+	24.4735i	0.512204	+	0.887164i	0.999900	+	0.0141502i	$0.00450429\pi$
$761$	14.1298	+	24.4735i	0.512204	+	0.887164i	−0.487696	+	0.873014i	$0.662162\pi$
$762$		0			0
$763$	−1.17705	+	2.03870i	−0.0426119	+	0.0738060i
$764$	−16.9519			−0.613299
$765$		0			0
$766$	−2.39407			−0.0865013
$767$	8.99180	−	15.5743i	0.324675	−	0.562354i
$768$		0			0
$769$	23.4518	+	40.6197i	0.845694	+	1.46478i	0.885017	+	0.465558i	$0.154146\pi$
$769$	23.4518	+	40.6197i	0.845694	+	1.46478i	−0.0393235	+	0.999227i	$0.512520\pi$
$770$		0			0
$771$		0			0
$772$	3.19791	−	5.53894i	0.115095	−	0.199351i
$773$	−9.19641			−0.330772			−0.165386	−	0.986229i	$-0.552887\pi$
$773$	−9.19641			−0.330772			−0.165386	+	0.986229i	$0.552887\pi$
$774$		0			0
$775$		0			0
$776$	−12.0414	+	20.8563i	−0.432260	+	0.748696i
$777$		0			0
$778$	−10.5458	−	18.2658i	−0.378085	−	0.654862i
$779$	15.1562	+	26.2512i	0.543025	+	0.940548i
$780$		0			0
$781$	−8.59074	+	14.8796i	−0.307401	+	0.532434i
$782$	38.1261			1.36339
$783$		0			0
$784$	32.9844			1.17801
$785$		0			0
$786$		0			0
$787$	−2.87319	−	4.97651i	−0.102418	−	0.177393i	0.810262	−	0.586067i	$-0.199325\pi$
$787$	−2.87319	−	4.97651i	−0.102418	−	0.177393i	−0.912680	+	0.408674i	$0.865991\pi$
$788$	−0.691939	−	1.19847i	−0.0246493	−	0.0426938i
$789$		0			0
$790$		0			0
$791$	6.06126			0.215514
$792$		0			0
$793$	−17.7411			−0.630004
$794$	0.709351	−	1.22863i	0.0251739	−	0.0436025i
$795$		0			0
$796$	−4.38128	−	7.58859i	−0.155290	−	0.268971i
$797$	−3.53725	−	6.12670i	−0.125296	−	0.217019i	0.796553	−	0.604569i	$-0.206655\pi$
$797$	−3.53725	−	6.12670i	−0.125296	−	0.217019i	−0.921849	+	0.387550i	$0.873321\pi$
$798$		0			0
$799$	−11.3095	+	19.5887i	−0.400103	+	0.692998i
$800$		0			0
$801$		0			0
$802$	−54.5868			−1.92753
$803$	18.2893	−	31.6781i	0.645417	−	1.11789i
$804$		0			0
$805$		0			0
$806$	−21.5515	−	37.3282i	−0.759118	−	1.31483i
$807$		0			0
$808$	18.8836	−	32.7074i	0.664323	−	1.15064i
$809$	−38.1075			−1.33979			−0.669894	−	0.742457i	$-0.733660\pi$
$809$	−38.1075			−1.33979			−0.669894	+	0.742457i	$0.733660\pi$
$810$		0			0
$811$	−1.44105			−0.0506022			−0.0253011	−	0.999680i	$-0.508054\pi$
$811$	−1.44105			−0.0506022			−0.0253011	+	0.999680i	$0.508054\pi$
$812$	−0.415754	+	0.720107i	−0.0145901	+	0.0252708i
$813$		0			0
$814$	−17.0351	−	29.5057i	−0.597081	−	1.03417i
$815$		0			0
$816$		0			0
$817$	−3.69698	+	6.40335i	−0.129341	+	0.224025i
$818$	8.25904			0.288771
$819$		0			0
$820$		0			0
$821$	11.2571	−	19.4979i	0.392876	−	0.680482i	−0.599951	−	0.800037i	$-0.704813\pi$
$821$	11.2571	−	19.4979i	0.392876	−	0.680482i	0.992828	+	0.119555i	$0.0381467\pi$
$822$		0			0
$823$	20.7295	+	35.9045i	0.722583	+	1.25155i	0.959961	+	0.280134i	$0.0903788\pi$
$823$	20.7295	+	35.9045i	0.722583	+	1.25155i	−0.237378	+	0.971417i	$0.576288\pi$
$824$	−0.905373	−	1.56815i	−0.0315402	−	0.0546291i
$825$		0			0
$826$	−1.18982	+	2.06083i	−0.0413992	+	0.0717055i
$827$	−27.8133			−0.967164			−0.483582	−	0.875299i	$-0.660664\pi$
$827$	−27.8133			−0.967164			−0.483582	+	0.875299i	$0.660664\pi$
$828$		0			0
$829$	20.7232			0.719745			0.359872	−	0.933002i	$-0.382820\pi$
$829$	20.7232			0.719745			0.359872	+	0.933002i	$0.382820\pi$
$830$		0			0
$831$		0			0
$832$	−11.9568	−	20.7098i	−0.414528	−	0.717983i
$833$	−20.5718	−	35.6314i	−0.712770	−	1.23455i
$834$		0			0
$835$		0			0
$836$	11.5537			0.399595
$837$		0			0
$838$	−17.9017			−0.618403
$839$	9.07253	−	15.7141i	0.313218	−	0.542510i	−0.665839	−	0.746096i	$-0.731926\pi$
$839$	9.07253	−	15.7141i	0.313218	−	0.542510i	0.979057	+	0.203585i	$0.0652595\pi$
$840$		0			0
$841$	11.4759	+	19.8768i	0.395720	+	0.685406i
$842$	8.69029	+	15.0520i	0.299487	+	0.518727i
$843$		0			0
$844$	−3.71722	+	6.43841i	−0.127952	+	0.221619i
$845$		0			0
$846$		0			0
$847$	0.701798			0.0241141
$848$	6.21591	−	10.7663i	0.213455	−	0.369716i
$849$		0			0
$850$		0			0
$851$	−12.8670	−	22.2862i	−0.441074	−	0.763962i
$852$		0			0
$853$	2.00354	−	3.47023i	0.0685999	−	0.118819i	−0.829685	−	0.558231i	$-0.811480\pi$
$853$	2.00354	−	3.47023i	0.0685999	−	0.118819i	0.898285	+	0.439413i	$0.144813\pi$
$854$	2.34755			0.0803316
$855$		0			0
$856$	24.0672			0.822599
$857$	−4.54485	+	7.87192i	−0.155249	+	0.268900i	−0.933150	−	0.359488i	$-0.882951\pi$
$857$	−4.54485	+	7.87192i	−0.155249	+	0.268900i	0.777901	+	0.628387i	$0.216285\pi$
$858$		0			0
$859$	−8.19348	−	14.1915i	−0.279558	−	0.484208i	0.691717	−	0.722169i	$-0.256855\pi$
$859$	−8.19348	−	14.1915i	−0.279558	−	0.484208i	−0.971275	+	0.237960i	$0.923521\pi$
$860$		0			0
$861$		0			0
$862$	−30.5122	+	52.8486i	−1.03925	+	1.80003i
$863$	−23.7967			−0.810050			−0.405025	−	0.914306i	$-0.632737\pi$
$863$	−23.7967			−0.810050			−0.405025	+	0.914306i	$0.632737\pi$
$864$		0			0
$865$		0			0
$866$	14.0602	−	24.3530i	0.477785	−	0.827549i
$867$		0			0
$868$	0.714850	+	1.23816i	0.0242636	+	0.0420258i
$869$	5.27496	+	9.13650i	0.178941	+	0.309935i
$870$		0			0
$871$	7.50747	−	13.0033i	0.254381	−	0.440600i
$872$	10.1291			0.343016
$873$		0			0
$874$	34.8137			1.17759
$875$		0			0
$876$		0			0
$877$	−18.0372	−	31.2413i	−0.609073	−	1.05495i	−0.991394	−	0.130916i	$-0.958208\pi$
$877$	−18.0372	−	31.2413i	−0.609073	−	1.05495i	0.382321	−	0.924030i	$-0.375125\pi$
$878$	25.9343	+	44.9196i	0.875241	+	1.51596i
$879$		0			0
$880$		0			0
$881$	35.4575			1.19459			0.597297	−	0.802020i	$-0.296241\pi$
$881$	35.4575			1.19459			0.597297	+	0.802020i	$0.296241\pi$
$882$		0			0
$883$	−39.1320			−1.31690			−0.658448	−	0.752626i	$-0.728787\pi$
$883$	−39.1320			−1.31690			−0.658448	+	0.752626i	$0.728787\pi$
$884$	12.7323	−	22.0531i	0.428235	−	0.741725i
$885$		0			0
$886$	−0.290768	−	0.503625i	−0.00976855	−	0.0169196i
$887$	25.6416	+	44.4126i	0.860962	+	1.49123i	0.871002	+	0.491280i	$0.163471\pi$
$887$	25.6416	+	44.4126i	0.860962	+	1.49123i	−0.0100402	+	0.999950i	$0.503196\pi$
$888$		0			0
$889$	−0.815778	+	1.41297i	−0.0273603	+	0.0473895i
$890$		0			0
$891$		0			0
$892$	−2.60530			−0.0872318
$893$	−10.3270	+	17.8868i	−0.345579	+	0.598560i
$894$		0			0
$895$		0			0
$896$	3.42207	+	5.92720i	0.114323	+	0.198014i
$897$		0			0
$898$	−6.41752	+	11.1155i	−0.214156	+	0.370928i
$899$	−10.3994			−0.346841
$900$		0			0
$901$	−15.5070			−0.516614
$902$	13.7811	−	23.8696i	0.458862	−	0.794772i
$903$		0			0
$904$	−13.0401	−	22.5861i	−0.433708	−	0.751204i
$905$		0			0
$906$		0			0
$907$	−23.9294	+	41.4470i	−0.794563	+	1.37622i	0.128552	+	0.991703i	$0.458967\pi$
$907$	−23.9294	+	41.4470i	−0.794563	+	1.37622i	−0.923116	+	0.384522i	$0.874366\pi$
$908$	−8.56930			−0.284382
$909$		0			0
$910$		0			0
$911$	9.02153	−	15.6258i	0.298897	−	0.517704i	−0.676987	−	0.735995i	$-0.736715\pi$
$911$	9.02153	−	15.6258i	0.298897	−	0.517704i	0.975884	+	0.218291i	$0.0700481\pi$
$912$		0			0
$913$	−21.5482	−	37.3226i	−0.713142	−	1.23520i
$914$	−17.5552	−	30.4065i	−0.580675	−	1.00576i
$915$		0			0
$916$	−2.22559	+	3.85483i	−0.0735354	+	0.127367i
$917$	−4.74276			−0.156620
$918$		0			0
$919$	10.3976			0.342984			0.171492	−	0.985185i	$-0.445141\pi$
$919$	10.3976			0.342984			0.171492	+	0.985185i	$0.445141\pi$
$920$		0			0
$921$		0			0
$922$	33.4854	+	57.9984i	1.10278	+	1.91008i
$923$	17.2892	+	29.9458i	0.569081	+	0.985676i
$924$		0			0
$925$		0			0
$926$	68.8351			2.26206
$927$		0			0
$928$	8.95410			0.293933
$929$	−18.0108	+	31.1956i	−0.590915	+	1.02349i	0.403194	+	0.915114i	$0.367900\pi$
$929$	−18.0108	+	31.1956i	−0.590915	+	1.02349i	−0.994109	+	0.108381i	$0.965433\pi$
$930$		0			0
$931$	−18.7845	−	32.5358i	−0.615638	−	1.06632i
$932$	−1.22382	−	2.11971i	−0.0400874	−	0.0694334i
$933$		0			0
$934$	−18.4101	+	31.8873i	−0.602398	+	1.04338i
$935$		0			0
$936$		0			0
$937$	24.0326			0.785111			0.392555	−	0.919728i	$-0.371591\pi$
$937$	24.0326			0.785111			0.392555	+	0.919728i	$0.371591\pi$
$938$	−0.993410	+	1.72064i	−0.0324360	+	0.0561808i
$939$		0			0
$940$		0			0
$941$	8.33380	+	14.4346i	0.271674	+	0.470553i	0.969291	−	0.245918i	$-0.0790894\pi$
$941$	8.33380	+	14.4346i	0.271674	+	0.470553i	−0.697616	+	0.716471i	$0.745756\pi$
$942$		0			0
$943$	10.4092	−	18.0292i	0.338969	−	0.587112i
$944$	14.0959			0.458783
$945$		0			0
$946$	6.72315			0.218589
$947$	−13.7700	+	23.8503i	−0.447464	+	0.775031i	−0.998220	−	0.0596355i	$-0.981006\pi$
$947$	−13.7700	+	23.8503i	−0.447464	+	0.775031i	0.550756	+	0.834666i	$0.314339\pi$
$948$		0			0
$949$	−36.8080	−	63.7533i	−1.19484	−	2.06952i
$950$		0			0
$951$		0			0
$952$	3.35154	−	5.80504i	0.108624	−	0.188142i
$953$	18.1344			0.587432			0.293716	−	0.955893i	$-0.405108\pi$
$953$	18.1344			0.587432			0.293716	+	0.955893i	$0.405108\pi$
$954$		0			0
$955$		0			0
$956$	−5.24922	+	9.09192i	−0.169772	+	0.294054i
$957$		0			0
$958$	−27.1917	−	47.0974i	−0.878523	−	1.52165i
$959$	−0.583565	−	1.01076i	−0.0188443	−	0.0326393i
$960$		0			0
$961$	6.55956	−	11.3615i	0.211599	−	0.366500i
$962$	−68.5676			−2.21071
$963$		0			0
$964$	7.51009			0.241884
$965$		0			0
$966$		0			0
$967$	−18.0937	−	31.3393i	−0.581855	−	1.00780i	−0.995259	−	0.0972552i	$-0.968994\pi$
$967$	−18.0937	−	31.3393i	−0.581855	−	1.00780i	0.413404	−	0.910548i	$-0.364340\pi$
$968$	−1.50984	−	2.61512i	−0.0485281	−	0.0840532i
$969$		0			0
$970$		0			0
$971$	34.6173			1.11092			0.555461	−	0.831542i	$-0.312542\pi$
$971$	34.6173			1.11092			0.555461	+	0.831542i	$0.312542\pi$
$972$		0			0
$973$	−5.50527			−0.176491
$974$	−19.4170	+	33.6312i	−0.622161	+	1.07761i
$975$		0			0
$976$	−6.95292	−	12.0428i	−0.222557	−	0.385481i
$977$	−14.7166	−	25.4898i	−0.470825	−	0.815492i	0.528618	−	0.848860i	$-0.322710\pi$
$977$	−14.7166	−	25.4898i	−0.470825	−	0.815492i	−0.999443	+	0.0333671i	$0.989377\pi$
$978$		0			0
$979$	−5.24729	+	9.08857i	−0.167704	+	0.290472i
$980$		0			0
$981$		0			0
$982$	7.52432			0.240111
$983$	12.2456	−	21.2099i	0.390573	−	0.676492i	−0.601953	−	0.798532i	$-0.705610\pi$
$983$	12.2456	−	21.2099i	0.390573	−	0.676492i	0.992525	+	0.122040i	$0.0389437\pi$
$984$		0			0
$985$		0			0
$986$	−12.2549	−	21.2260i	−0.390274	−	0.675975i
$987$		0			0
$988$	11.6262	−	20.1371i	0.369878	−	0.640647i
$989$	5.07813			0.161475
$990$		0			0
$991$	−13.2821			−0.421919			−0.210959	−	0.977495i	$-0.567659\pi$
$991$	−13.2821			−0.421919			−0.210959	+	0.977495i	$0.567659\pi$
$992$	7.69787	−	13.3331i	0.244408	−	0.423327i
$993$		0			0
$994$	−2.28776	−	3.96251i	−0.0725632	−	0.125683i
$995$		0			0
$996$		0			0
$997$	−19.5765	+	33.9075i	−0.619994	+	1.07386i	0.369492	+	0.929234i	$0.379532\pi$
$997$	−19.5765	+	33.9075i	−0.619994	+	1.07386i	−0.989486	+	0.144627i	$0.953802\pi$
$998$	−30.8734			−0.977280
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.e.e.451.1		8
3.2	odd	2		225.2.e.c.151.4	yes	8
5.2	odd	4		675.2.k.c.424.2		16
5.3	odd	4		675.2.k.c.424.7		16
5.4	even	2		675.2.e.c.451.4		8
9.2	odd	6		2025.2.a.y.1.1		4
9.4	even	3	inner	675.2.e.e.226.1		8
9.5	odd	6		225.2.e.c.76.4	✓	8
9.7	even	3		2025.2.a.p.1.4		4
15.2	even	4		225.2.k.c.124.7		16
15.8	even	4		225.2.k.c.124.2		16
15.14	odd	2		225.2.e.e.151.1	yes	8
45.2	even	12		2025.2.b.n.649.2		8
45.4	even	6		675.2.e.c.226.4		8
45.7	odd	12		2025.2.b.o.649.7		8
45.13	odd	12		675.2.k.c.199.2		16
45.14	odd	6		225.2.e.e.76.1	yes	8
45.22	odd	12		675.2.k.c.199.7		16
45.23	even	12		225.2.k.c.49.7		16
45.29	odd	6		2025.2.a.q.1.4		4
45.32	even	12		225.2.k.c.49.2		16
45.34	even	6		2025.2.a.z.1.1		4
45.38	even	12		2025.2.b.n.649.7		8
45.43	odd	12		2025.2.b.o.649.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.4	✓	8	9.5	odd	6
225.2.e.c.151.4	yes	8	3.2	odd	2
225.2.e.e.76.1	yes	8	45.14	odd	6
225.2.e.e.151.1	yes	8	15.14	odd	2
225.2.k.c.49.2		16	45.32	even	12
225.2.k.c.49.7		16	45.23	even	12
225.2.k.c.124.2		16	15.8	even	4
225.2.k.c.124.7		16	15.2	even	4
675.2.e.c.226.4		8	45.4	even	6
675.2.e.c.451.4		8	5.4	even	2
675.2.e.e.226.1		8	9.4	even	3	inner
675.2.e.e.451.1		8	1.1	even	1	trivial
675.2.k.c.199.2		16	45.13	odd	12
675.2.k.c.199.7		16	45.22	odd	12
675.2.k.c.424.2		16	5.2	odd	4
675.2.k.c.424.7		16	5.3	odd	4
2025.2.a.p.1.4		4	9.7	even	3
2025.2.a.q.1.4		4	45.29	odd	6
2025.2.a.y.1.1		4	9.2	odd	6
2025.2.a.z.1.1		4	45.34	even	6
2025.2.b.n.649.2		8	45.2	even	12
2025.2.b.n.649.7		8	45.38	even	12
2025.2.b.o.649.2		8	45.43	odd	12
2025.2.b.o.649.7		8	45.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.816862 + 1.41485i) q^{2} +(-0.334526 - 0.579416i) q^{4} +(0.252674 - 0.437645i) q^{7} -2.17440 q^{8} +(1.55010 - 2.68485i) q^{11} +(-3.11964 - 5.40337i) q^{13} +(0.412800 + 0.714990i) q^{14} +(2.44524 - 4.23527i) q^{16} -6.10020 q^{17} -5.57022 q^{19} +(2.53244 + 4.38631i) q^{22} +(1.91280 + 3.31307i) q^{23} +10.1932 q^{26} -0.338104 q^{28} +(1.22966 - 2.12984i) q^{29} +(-2.11429 - 3.66206i) q^{31} +(1.82044 + 3.15309i) q^{32} +(4.98302 - 8.63085i) q^{34} -6.72677 q^{37} +(4.55010 - 7.88101i) q^{38} +(-2.72092 - 4.71278i) q^{41} +(0.663704 - 1.14957i) q^{43} -2.07420 q^{44} -6.24997 q^{46} +(1.85396 - 3.21115i) q^{47} +(3.37231 + 5.84101i) q^{49} +(-2.08720 + 3.61514i) q^{52} +2.54205 q^{53} +(-0.549415 + 0.951614i) q^{56} +(2.00893 + 3.47956i) q^{58} +(1.44116 + 2.49616i) q^{59} +(1.42173 - 2.46250i) q^{61} +6.90833 q^{62} +3.83276 q^{64} +(1.20326 + 2.08411i) q^{67} +(2.04068 + 3.53456i) q^{68} -5.54205 q^{71} +11.7988 q^{73} +(5.49484 - 9.51734i) q^{74} +(1.86338 + 3.22748i) q^{76} +(-0.783341 - 1.35679i) q^{77} +(-1.70149 + 2.94707i) q^{79} +8.89047 q^{82} +(6.95059 - 12.0388i) q^{83} +(1.08431 + 1.87808i) q^{86} +(-3.37054 + 5.83795i) q^{88} -3.38513 q^{89} -3.15301 q^{91} +(1.27976 - 2.21661i) q^{92} +(3.02886 + 5.24614i) q^{94} +(5.53779 - 9.59173i) q^{97} -11.0188 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{4} + q^{7} - 18 q^{8} - q^{11} - 2 q^{13} + 3 q^{14} - 4 q^{16} - 22 q^{17} + 4 q^{19} - 3 q^{22} + 15 q^{23} + 20 q^{26} - 8 q^{28} + q^{29} + 4 q^{31} + 10 q^{32} - 9 q^{34} - 2 q^{37}+ \cdots - 26 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 4 * q^4 + q^7 - 18 * q^8 - q^11 - 2 * q^13 + 3 * q^14 - 4 * q^16 - 22 * q^17 + 4 * q^19 - 3 * q^22 + 15 * q^23 + 20 * q^26 - 8 * q^28 + q^29 + 4 * q^31 + 10 * q^32 - 9 * q^34 - 2 * q^37 + 23 * q^38 - 5 * q^41 + 10 * q^43 - 44 * q^44 + 20 * q^47 + 3 * q^49 - 17 * q^52 - 40 * q^53 - 30 * q^56 + 18 * q^58 + 17 * q^59 + 13 * q^61 + 12 * q^62 + 38 * q^64 - 17 * q^67 + 34 * q^68 + 16 * q^71 + 4 * q^73 + 40 * q^74 - 11 * q^76 + 12 * q^77 + 7 * q^79 + 24 * q^82 + 30 * q^83 - 34 * q^86 - 9 * q^88 + 18 * q^89 - 34 * q^91 - 12 * q^92 - 3 * q^94 + 19 * q^97 - 26 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more